D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y First Integrated Magnetic and Kinetic Control for AT Scenarios on DIII-D D. Moreau CEA-DSM-IRFM, Cadarache, St-Paul-lez-Durance Cedex, France E. Schuster, J. Barton, D. Boyer, W. Shi, W. Wehner Lehigh University, Bethlehem, PA 18015, USA M. Walker, J. Ferron, D. Humphreys, A. Hyatt, B. Johnson, B. Penaflor, F. Turco, and many DIII-D collaborators General Atomics, San Diego, CA 92186, USA 1 ITPA-IOS Joint Experiment # 6.1

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Outline ARTAEMIS model structure and integrated control Control of the internal poloidal flux profile,  (x) Integrated control of  (x) and  N Lehigh University controller and  (x) control Proposal for 2012 and beyond 2

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y The ARTAEMIS (grey-box) model-based approach D. Moreau et al., Nucl. Fusion 48 (2008) ARTAEMIS is a set of algorithms that use singular perturbation methods : (i)a semi-empirical system identification method (ii)a model-based, 2-time-scale, control algorithm for magneto-kinetic plasma state What could a minimal state space model look like ? Are there natural state variables and input variables ? How are they coupled ? etc … Generic structure of linearized flux-averaged plasma transport equations :

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y The ARTAEMIS controller design and parameters for combined  (x) and  N control 4 Singular perturbation analysis  Near-optimal control = Optimal control up to O(  2 ) The dynamics minimizes using a given set of SVD modes (controller order) minimizes The slow proportional + integral feedback tracks a steady state that The fast proportional feedback loop maintains the kinetic variables, e. g.  N, on a trajectory which is consistent with the slow magnetic state evolution,  (x, t). given weight matrices, Q and R, with X = controlled variables and u = actuators to control simultaneously  (x) and  N minimizes

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Control of the internal poloidal flux profile :  (x) =  (x) –  boundary 5 The controller minimizes with actuator constraints and optimal gain matrices that depend on controller parameters : 4 actuators = NB-Co, NB-Bal, ECCD (5 gyros), Vsurf (NB 210R unavailable on 09/13) R-matrix : actuator weight fixed by considering actuator headroom (MW & Volts ?) Q-matrix : same weight on 9 different controlled radii (x = 0.1, …, 0.9) Controller order = 2 (proportional + integral control) Weight on integral control in the Q-matrix = 4, 10, 25, respectively, on the 3 examples below : # : IntWeight = 4# : IntWeight = 10# : IntWeight = 25

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Control of the poloidal flux profile (x = 0.1, 0.2, … 0.9) 6 # : IntWeight = 4# : IntWeight = 10# : IntWeight = 25 Control : 3.5 s - 6 sControl : 3.5 s - 5 sControl : 2.5 s - 6 s x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Control of the poloidal flux profile  t = 2.5 s, 4 s, 6 s 7 # : IntWeight = 4# : IntWeight = 25 SlowFast (overshoot)

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y with actuator constraints and optimal gain matrices that depend on controller parameters : 5 actuators = NB-Co, NB-Bal, NB-Cnt, ECCD (6 gyros), Vsurf R-matrix : actuator weights fixed by considering actuator headroom (MW & Volts ?) Q-matrix : same weight on 9 controlled radii for  (x), x=0.1, 0.2, … 0.9 Weight on  N control : = 0.3 Controller order = 2 or 3 (proportional + integral control) Weight on integral control in the Q-matrix = 25 and 10, respectively, in the 2 examples below : Actuator saturation Simultaneous control of the  (x) profile and  N 5 actuators : NB-co, NB-bal, NB-cnt, ECCD, Vsurf 8 The controller minimizes # Control order = 2 IntWeight = 25 # Control order = 3 IntWeight = 10 MHD

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9 radii Simultaneous control of the  (x) profile and  N (shot # : control t = 1.5 s) 9  N control  -profile control  (x= 0.1, 0.2, …0.9) & targets (lines) Time

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Simultaneous control of the  (x) profile and  N (shot # : control t = 1.5 s) 10 5 actuators (no saturation) Vsurf actuator control & Ip Cost function minimization

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y MHD Ip Simultaneous control of the  (x) profile and  N shot # : control t = 1 s (ramp-up) 11  N control  -profile control x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9 radii  (x= 0.1, 0.2, …0.9) & targets (lines) Time

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Simultaneous control of the  (x) profile and  N shot # : control t = 1 s (ramp-up) 12 5 actuators (MHD  NB-Bal saturation) Vsurf actuator control & Ip Cost function minimization

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y 13 Lehigh University Approach to Feedback Control Design: Data-driven Model-based Current Profile Control –Both static and dynamic control-oriented plasma response models are embedded in the control synthesis. –A cost functional is defined to quantify the control objectives: Tracking error minimization Disturbance rejection Control power minimization –Stabilizing controllers, which are robust against model uncertainties, are synthesized by minimizing different norms (H ∞ and H 2 norms) of the cost functional subject to the control-oriented model. –These controllers do not need PID-like empirical tuning. –The controllers are augmented with model-based anti-windup compensators to overcome detriments effects due to actuator saturation.

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y 14 Data-driven Model-based Control of  (x) =1/q(x) –In the DIII-D PCS different magnetic profiles (  (  ),  (  ), q(  ) or  (  )=  /  ) can now be obtained in real time from a complete equilibrium reconstruction using data from the MSE diagnostic. –Figure on the left illustrates both simulated and experimental evolutions for the rotational transform  (  ) at normalized radii  =0.2, 0.4, 0.5, 0.6, 0.8 for shot –Tracking of the  (  ) target profile was achieved by regulating: Total plasma current Co-injection and balanced beam powers (counter-injection beam not available) Total ECH/ECCD power –Artificial input disturbances were introduced at t=3.5 sec.

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y 15 Data-driven Model-based Control of  (x) =1/q(x) Tight regulation is achieved before t=3.5 sec. A significant tracking error in the inner part of the profile is noted after the artificial disturbance is introduced at t=3.5 sec. The controller reacts by decreasing the tracking error at the inner point and slightly increasing the error at the outer points with the ultimate goal of improving the overall profile tracking. Ip regulation was poor due to setup problem. More control authority is expected with stronger Ip regulation and counter injection beam.

D. Moreau, ITPA-IOS Meeting, Kyoto, October 18-21, 2011 LEHIGH U N I V E R S I T Y Control of  (x),  (x) = 1/q(x) and combined control of  (x) and  N have been achieved for the first time on DIII-D using either 4 or 5 actuators : Co-NBI, (Cnt-NBI), Bal-NBI, ECCD, Vsurf New PCS with profile control algorithm was qualified and worked perfectly  (x) and  N control was switched on during current ramp-up. Combined feedback control of  (x) and  N was successful up to [1s-6s] Proposal for ITPA-IOS 2012 : Integrated magnetic and kinetic plasma control More experiments on DIII-D with different target current profiles and  N. Add control of the rotation and/or Ti profiles (real-time CER) Start profile control experiments on other devices (Tore Supra, TCV …?) Summary and proposal for 2012 … 16